A paean to Approval voting – "Count all the votes"

By
Warren D. Smith.
Also incorporates some ideas and/or verbatim sentences from
Steven J. Brams,
Catherine Kimport,
Mike Ossipoff,
Andrew Jennings, and Abd ul-Rahman Lomax.
However, Brams may not entirely agree with the present page. The
essay by Brams from which many sentences have been lifted verbatim (or nearly),
is here. We in turn do not entirely agree with that essay.
Brams is the coauthor of the book Approval Voting.
See also Sanders' essay.

The simplest way to introduce approval voting to those
familiar with the current plurality system
is with the slogan "count all the votes."
That is, if somebody in the current system votes for Nader and Bush,
then her vote is discarded as an illegal "overvote" and not counted.
With approval voting, overvotes are legal and all votes are counted.

So it is just like the current system, only SIMPLER, and it
works with all today's voting equipment
with no modification and no reprogramming needed.

If you want some other kind of voting reform, you definitely should want approval voting, because
it gets a long way in the direction you want,
doesn't hurt you, and it is so incredibly simple and easy.

Formal definition:

In Approval Voting (AV), each voter approves or disapproves of every candidate.

The most-approved candidate wins.

Set voting

Approval voting has also been called "set voting" because voters vote for whichever
set of
candidates they prefer versus the candidates they don't vote for.
In this graphic, we can see there are 8 possible kinds of voters: those who approve
Nader only, those who approve Gore only, those approving both Nader & Gore
(but not Bush), and so on.
With approval voting, all 8 kinds are capable of saying in their vote, which kind they are,
and the election result takes account of how many voters of each kind are present.
With old-fashioned plain-plurality voting, though, that information simply is not available
and cannot be used to to help make the election decision.

Variants to try to make approval voting even better

1. We could add intermediate options between full approval and full disapproval.
When you do that, you get range voting.
The advantages of range voting versus AV are summarized here.

2. We could also, optionally, permit voters to express no opinion about a candidate.
That is useful because a lot of voters are ignorant about a lot of candidates and
in some cases would prefer to leave the decision about rating that candidate, to other,
hopefully more-informed, voters.
(In fact,
there is evidence
that the vast majority of US voters who are offered the chance
to vote about judges, know essentially nothing
about those judges.)
The definition of range voting given on the
main page in fact already incorporates the "no opinion"
idea, and we could
also add it to approval voting.

Indeed, AV then really is just the special case of range voting (with or without
"no opinion" scores permitted)
in which the only allowed scores are 0 (disapprove) and 1 (approve).

3. Forest Simmons invented DYN (for Delegable Yes/No) voting.
It is similar to Approval but more complicated to count.
(Almost as simple for the voter, however!)
A related followup idea invented by Jameson Quinn was SODA voting.
DYN's virtue is immunity to "media manipulation" of poll data;
the question then is whether the extra complexity of DYN is worth the benefits arising
from this immunity.

Approval overcomes a major flaw in plurality voting (while making it simpler)

In any race with more than two candidates, plurality
may elect
the candidate least acceptable to the majority of voters.
This frequently happens in a three-way contest, when the majority splits its votes
between two centrist candidates, allowing a more extreme candidate to win.
Plurality also forces minor-party candidates into the role of
spoilers,
as we saw in USA 2000,
which can be decisive in a close contest between the
major-party candidates.
That in turn causes many voters to refuse to vote for their true favorite (!) unless it coincides
with one of the two candidates that seem most likely to win – out
of a (justified) fear of creating a "spoiler" or "wasted vote" scenario.
And that in turn causes third parties to die out over time, causing
2-party domination, which severely reduces voter choice and thus
makes democracy work badly.

Approval gives voters much more expressivity

Instead of "name one candidate, then shut up," it is
"express a yes/no opinion on all the candidates."
You the voter, get to say much more. Why should less of your views be incorporated,
when more of them can be?

Approval gives voters more power

Say we want to define a notion of "voting power."
What quantity would make sense as that voting power?
One way is to measure
the number of pairs of candidates of unequal merit
that your vote can discriminate between. The more such pairs there are,
the more chance your vote will be able to have an effect by breaking a tie between that pair.
(If there is no tie, then your vote has no effect.)

With plurality voting, your vote-for-one discriminates that one candidate versus the other N-1,
for a "voting power" of N-1. With approval voting, you can approve of half the N candidates,
discriminating N/2 of them from the other N/2, for a voting power of N²/4.
The ratio between these two voting powers is
N²/(4N-4). We exhibit that formula in this table:

N=#candidates

Voting Power Ratio

2

1

3

1.125

4

1.333

5

1.563

6

1.800

7

2.042

8

2.286

9

2.531

10

2.778

20

5.363

50

12.76

100

25.25

Approval voting is excellent for use in votes in meetings

You can just hold up your
hand (or better, a red card) to approve of an option.

Actually, range voting on a 3-point scale {0,1,2} could also be thus-conducted using
two red cards per voter, and a voter could hold
them up using either zero, one, or two hands.

This is much simpler than
plurality voting, where if you tried hand-raising voting, you'd pretty
much have to trust people not to cheat by overvoting, since careful verification
takes ages. Approval is the fastest, simplest, and most reliable
method for voting in meetings.

What might an approval ballot look like?

An AV ballot could look almost exactly like a Plurality ballot.
Here's a quick side-by-side comparison:

Plurality Vote

What is your favorite color?

Red
Orange
Yellow
Green
Blue
Violet
Black
White

Approval Vote

Which colors do you like?

Red
Orange
Yellow
Green
Blue
Violet
Black
White

A ballot for the variant-approval system (also allowing "no opinion" votes) could be like this:

Approval Vote II –
Which colors do you like?

Color

Yes

No

"no opinion"

RED

•

Ο

Ο

ORANGE

•

Ο

Ο

YELLOW

•

Ο

Ο

GREEN

Ο

•

Ο

BLUE

•

Ο

Ο

INDIGO

Ο

•

Ο

VIOLET

•

Ο

Ο

WHITE

Ο

Ο

•

Approval voting history

Approval and Range voting were the foundation of government in
renaissance Venice,
and Ancient Sparta respectively, two of the longest lasting (perhaps
the two longest lasting) democracies ever. Also approval voting was
used for centuries to elect the catholic pope (at the time the most
powerful elected person on the planet) and
was used in 1000s of elections in the USSR, and was used to elect the
first 4 USA presidencies and is currently used to elect the UN
secretary-general.
(Approximately. The rules were slightly different in most of these cases, e.g.
the first 4 US presidential elections had the undesirable twist that the second-place
finisher became the vice president.)

Approval voting was apparently first explicitly invented in the modern era by
Guy Ottewell in 1968 (albeit
Ottewell has now endorsed range voting).
Several political scientists and mathematicians
then invented it independently during the 1970s.
All of them at the time were unaware of that vast previous history.
Two of them, S.Brams and P.Fishburn, published a book on it in 1983.

AV has been used in internal elections by the political parties in some US states,
such as Pennsylvania, where a presidential straw poll using AV was conducted by the
Democratic State Committee in 1983.
Bills to implement AV have been introduced in several state legislatures.
In 1987, a bill to enact AV in certain statewide elections passed the Senate but not the
House in North Dakota. In 1990, Oregon used AV in a statewide advisory referendum on
school financing, which presented voters with five different options and allowed them to
vote for as many as they wished.

Since 1979, approval voting has been used in China
in the elections of its National People's Congress.

In the late 1980s, AV was used in thousands of competitive elections in countries in
Eastern Europe and the Soviet Union
(experiment in democratization initiated by M.Gorbachev)
where it was effectively "disapproval voting"
because voters were permitted to cross off names on ballots but
not to vote for candidates.
This procedure is logically equivalent to AV: candidates not crossed off are,
in effect, approved of. However psychologically there is almost
surely a difference
between approving and disapproving of candidates.

Beginning in 1987, several scientific and engineering societies adopted
AV:

Mathematical Association of America (MAA),
with about 32,000 members;

American Mathematical Society (AMS), with about
30,000 members;

Institute for Operations Research and Management
Sciences (INFORMS), with about 12,000 members;

American Statistical Association (ASA), with
about 15,000 members;

Institute of Electrical and Electronics Engineers
(IEEE), with about 377,000
members.

Smaller societies that use AV include the Society for Judgment and Decision
Making, the Social Choice and Welfare Society, the International Joint
Conference on Artificial Intelligence, the Pubic Choice Society,
and the European Association for
Logic, Language and Information.

In the early 2000s the
Boston Tea Party became
apparently the first US political party
in modern times to employ approval voting.

Additionally, the Econometric Society has used AV (with certain emendations)
to elect fellows since 1980; likewise, since 1981 the selection of members
of the National Academy of Sciences at the final stage of balloting has
been based on AV.
Coupled with many colleges and universities that now
use AV – from the departmental level to the school-wide level –
at least several hundred thousand individuals have
had direct experience with AV.

Click these links to learn about the French study of AV
and the other French study of Range Voting conducted during
two real French Presidential elections.
(See also
France 2012 election.)
"Approval ratings" are nowadays produced
all the time
by pollsters such as Gallup for various political candidates, which allows
you to tell
approximately what would happen in an election if it were run with approval voting.

Further comments

What about the "one person, one vote" principle?
Approval voting can instead be thought of as implementing the more-fair principle that
"one person gets one vote on each candidate."
Another way to think of it is: it still is one person one vote, it is just
that a "vote" is now a different thing – but still preserving the central
idea that a "vote" is an expression of your views, it is now just a better
expression of them. (And with range voting, even better still.)
This, e.g, affords voters an opportunity to express their intensities
of preference by approving of, for example, all candidates except the
one they despise.

Incidentally, there is nothing unconstitutional about approval voting.
The US constitution
intentionally did not
specify any voting method,
and its writers were well aware there were many possible voting
methods, and in fact approval voting basically
was used in the first few USA presidential elections
and several other (often more peculiar) voting methods have been used throughout US history.

You can also regard approval as obeying the same one-person-one-vote principle as plurality
voting as follows: only one of your votes gets used: the one indicating
your approval (or disapproval) of whoever wins the election.

Although AV encourages sincere voting, it does not altogether eliminate
strategic calculations. Because approval of a less-preferred candidate
can hurt a more-preferred approved candidate, the voter is still faced
with the decision of where to draw the line between acceptable and nonacceptable
candidates. A rational voter will vote for a second choice if his or her
first choice appears to be a long shot – as indicated, for example, by
polls – but the voter's calculus and its effects on outcomes is not yet
entirely understood either for AV or especially for more complicated voting procedures.

While AV is a strikingly simple election reform for finding consensus choices in single-winner elections, in elections with more than one winner
AV is not recommended
if the goal is to mirror a diversity of views, especially of minorities; for this purpose, other voting systems should be considered.
However Fishburn and Smith both have shown with computer simulations that approval still works
well in 2-winner situations where a "second round" election is used to decide between the
two winners in round 1.
On the other hand, minorities may derive indirect benefit from AV in single-winner elections, because mainstream candidates, in order to win, will be forced to reach out to minority voters for the approval they (the mainstream candidates) need to win. While promoting majoritarian candidates, therefore,
AV still induces them to be responsive to minority views.